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Articles 61 - 90 of 2315
Full-Text Articles in Physical Sciences and Mathematics
How To Gauge Inequality And Fairness: A Complete Description Of All Decomposable Versions Of Theil Index, Saeid Tizpaz-Niari, Olga Kosheleva, Vladik Kreinovich
How To Gauge Inequality And Fairness: A Complete Description Of All Decomposable Versions Of Theil Index, Saeid Tizpaz-Niari, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In general, in statistics, the most widely used way to describe the difference between different elements of a sample if by using standard deviation. This characteristic has a nice property of being decomposable: e.g., to compute the mean and standard deviation of the income overall the whole US, it is sufficient to compute the number of people, mean, and standard deviation over each state; this state-by-state information is sufficient to uniquely reconstruct the overall standard deviation. However, e.g., for gauging income inequality, standard deviation is not very adequate: it provides too much weight to outliers like billionaires, and thus, does …
Update From Aristotle To Newton, From Sets To Fuzzy Sets, And From Sigmoid To Relu: What Do All These Transitions Have In Common?, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Update From Aristotle To Newton, From Sets To Fuzzy Sets, And From Sigmoid To Relu: What Do All These Transitions Have In Common?, Christian Servin, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In this paper, we show that there is a -- somewhat unexpected -- common trend behind several seemingly unrelated historic transitions: from Aristotelian physics to modern (Newton's) approach, from crisp sets (such as intervals) to fuzzy sets, and from traditional neural networks, with close-to-step-function sigmoid activation functions to modern successful deep neural networks that use a completely different ReLU activation function. In all these cases, the main idea of the corresponding transition can be explained, in mathematical terms, as going from the first order to second order differential equations.
How To Make A Decision Under Interval Uncertainty If We Do Not Know The Utility Function, Jeffrey Escamilla, Vladik Kreinovich
How To Make A Decision Under Interval Uncertainty If We Do Not Know The Utility Function, Jeffrey Escamilla, Vladik Kreinovich
Departmental Technical Reports (CS)
Decision theory describes how to make decisions, in particular, how to make decisions under interval uncertainty. However, this theory's recommendations assume that we know the utility function -- a function that describes the decision maker's preferences. Sometimes, we can make a recommendation even when we do not know the utility function. In this paper, we provide a complete description of all such cases.
Paradox Of Causality And Paradoxes Of Set Theory, Alondra Baquier, Bradley Beltran, Gabriel Miki-Silva, Olga Kosheleva, Vladik Kreinovich
Paradox Of Causality And Paradoxes Of Set Theory, Alondra Baquier, Bradley Beltran, Gabriel Miki-Silva, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Logical paradoxes show that human reasoning is not always fully captured by the traditional 2-valued logic, that this logic's extensions -- such as multi-valued logics -- are needed. Because of this, the study of paradoxes is important for research on multi-valued logics. In this paper, we focus on paradoxes of set theory. Specifically, we show their analogy with the known paradox of causality, and we use this analogy to come up with similar set-theoretic paradoxes.
Number Representation With Varying Number Of Bits, Anuradha Choudhury, Md Ahsanul Haque, Saeefa Rubaiyet Nowmi, Ahmed Ann Noor Ryen, Sabrina Saika, Vladik Kreinovich
Number Representation With Varying Number Of Bits, Anuradha Choudhury, Md Ahsanul Haque, Saeefa Rubaiyet Nowmi, Ahmed Ann Noor Ryen, Sabrina Saika, Vladik Kreinovich
Departmental Technical Reports (CS)
In a computer, usually, all real numbers are stored by using the same number of bits: usually, 8 bytes, i.e., 64 bits. This amount of bits enables us to represent numbers with high accuracy -- up to 19 decimal digits. However, in most cases -- whether we process measurement results or whether we process expert-generated membership degrees -- we do not need that accuracy, so most bits are wasted. To save space, it is therefore reasonable to consider representations with varying number of bits. This would save space used for representing numbers themselves, but we would also need to store …
How To Fairly Allocate Safety Benefits Of Self-Driving Cars, Fernando Munoz, Christian Servin, Vladik Kreinovich
How To Fairly Allocate Safety Benefits Of Self-Driving Cars, Fernando Munoz, Christian Servin, Vladik Kreinovich
Departmental Technical Reports (CS)
In this paper, we describe how to fairly allocated safety benefits of self-driving cars between drivers and pedestrians -- so as to minimize the overall harm.
Using Known Relation Between Quantities To Make Measurements More Accurate And More Reliable, Niklas Winnewisser, Felix Mett, Michael Beer, Olga Kosheleva, Vladik Kreinovich
Using Known Relation Between Quantities To Make Measurements More Accurate And More Reliable, Niklas Winnewisser, Felix Mett, Michael Beer, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Most of our knowledge comes, ultimately, from measurements and from processing measurement results. In this, metrology is very valuable: it teaches us how to gauge the accuracy of the measurement results and of the results of data processing, and how to calibrate the measuring instruments so as to reach the maximum accuracy. However, traditional metrology mostly concentrates on individual measurements. In practice, often, there are also relations between the current values of different quantities. For example, there is usually an known upper bound on the difference between the values of the same quantity at close moments of time or at …
Data Fusion Is More Complex Than Data Processing: A Proof, Robert Alvarez, Salvador Ruiz, Martine Ceberio, Vladik Kreinovich
Data Fusion Is More Complex Than Data Processing: A Proof, Robert Alvarez, Salvador Ruiz, Martine Ceberio, Vladik Kreinovich
Departmental Technical Reports (CS)
Empirical data shows that, in general, data fusion takes more computation time than data processing. In this paper, we provide a proof that data fusion is indeed more complex than data processing.
Towards An Optimal Design: What Can We Recommend To Elon Musk?, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich, Hung T. Nguyen
Towards An Optimal Design: What Can We Recommend To Elon Musk?, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich, Hung T. Nguyen
Departmental Technical Reports (CS)
Elon Musk's successful "move fast and break things" strategy is based on the fact that in many cases, we do not need to satisfy all usual constraints to be successful. By sequentially trying smaller number of constraints, he finds the smallest number of constraints that are still needed to succeed -- and using this smaller number of constrains leads to a much cheaper (and thus, more practical) design. In this strategy, Musk relies on his intuition -- which, as all intuitions, sometimes works and sometimes doesn't. To replace this intuition, we propose an algorithm that minimizes the worst-case cost of …
Why Pavement Cracks Are Mostly Longitudinal, Sometimes Transversal, And Rarely Of Other Directions: A Geometric Explanation, Edgar Daniel Rodriguez Velasquez, Olga Kosheleva, Vladik Kreinovich
Why Pavement Cracks Are Mostly Longitudinal, Sometimes Transversal, And Rarely Of Other Directions: A Geometric Explanation, Edgar Daniel Rodriguez Velasquez, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In time, pavements deteriorate, and need maintenance. One of the most typical pavement faults are cracks. Empirically, the most frequent cracks are longitudinal, i.e., following the direction of the road; less frequent are transversal cracks, which are orthogonal to the direction of the road. Sometimes, there are cracks in different directions, but such cracks are much rarer. In this paper, we show that simple geometric analysis and fundamental physical ideas can explain these observed relative frequencies.
Why Two Fish Follow Each Other But Three Fish Form A School: A Symmetry-Based Explanation, Shahnaz Shahbazova, Olga Kosheleva, Vladik Kreinovich
Why Two Fish Follow Each Other But Three Fish Form A School: A Symmetry-Based Explanation, Shahnaz Shahbazova, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Recent experiments with fish has shown an unexpected strange behavior: when two fish of the same species are placed in an aquarium, they start following each other, while when three fish are placed there, they form (approximately) an equilateral triangle, and move in the direction (approximately) orthogonal to this triangle. In this paper, we use natural symmetries -- such as rotations, shifts, and permutation of fish -- to show that this observed behavior is actually optimal. This behavior is not just optimal with respect to one specific optimality criterion, it is optimal with respect to any optimality criterion -- as …
Predictive Understanding Of Lake Water Temperature And Dissolved Oxygen Profiles Across The Red River Basin Through Interpretable Machine Learning, Isabela Suaza Sierra
Predictive Understanding Of Lake Water Temperature And Dissolved Oxygen Profiles Across The Red River Basin Through Interpretable Machine Learning, Isabela Suaza Sierra
Open Access Theses & Dissertations
Accurately predicting lake water temperature (LWT) and dissolved oxygen (DO) is crucial for determining threshold values of fish survivability under warmer global conditions, with recreational fishing in reservoirs significantly contributing to regional economies, such as $779 million and $1,891 million annually to the economies of Oklahoma and Texas, respectively. Current mathematical models for temperature and oxygen profiles, which incorporate multi-layer and turbulent mixing equations, are complex and challenging to parameterize, particularly due to uncertainties in acquiring sufficient data for training and validation. Leveraging the flexibility and information extraction power of machine learning (ML) methods, this master thesis aimed to set …
Why Linear And Sigmoid Last Layers Work Better In Classification, Lehel Dénes-Fazakas, Lásló Szilágyi, Vladik Kreinovich
Why Linear And Sigmoid Last Layers Work Better In Classification, Lehel Dénes-Fazakas, Lásló Szilágyi, Vladik Kreinovich
Departmental Technical Reports (CS)
Usually, when a deep neural network is used to classify objects, its last layer computes the softmax. Our empirical results show we can improve the classification results if instead, we have linear or sigmoid last layer. In this paper, we provide an explanation for this empirical phenomenon.
Fuzzy Ideas Explain Fechner Law And Help Detect Relation Between Objects In Video, Olga Kosheleva, Vladik Kreinovich, Ahnaf Farhan
Fuzzy Ideas Explain Fechner Law And Help Detect Relation Between Objects In Video, Olga Kosheleva, Vladik Kreinovich, Ahnaf Farhan
Departmental Technical Reports (CS)
How to find relation between objects in a video? If two objects are closely related -- e.g., a computer and it mouse -- then they almost always appear together, and thus, their numbers of occurrences are close. However, simply computing the differences between numbers of occurrences is not a good idea: objects with 100 and 110 occurrences are most probably related, but objects with 1 and 5 occurrences probably not, although 5 − 1 is smaller than 110 − 100. A natural idea is, instead, to compute the difference between re-scaled numbers of occurrences, for an appropriate nonlinear re-scaling. In …
There Is Still Plenty Of Room At The Bottom: Feynman's Vision Of Quantum Computing 65 Years Later, Alexis Lupo, Vladik Kreinovich, Victor L. Timchenko, Yuriy P. Kondratenko
There Is Still Plenty Of Room At The Bottom: Feynman's Vision Of Quantum Computing 65 Years Later, Alexis Lupo, Vladik Kreinovich, Victor L. Timchenko, Yuriy P. Kondratenko
Departmental Technical Reports (CS)
In 1959, Nobelist Richard Feynman gave a talk titled "There's plenty of room at the bottom", in which he emphasized that, to drastically speed up computations, we need to make computer components much smaller -- all the way to the size of molecules, atoms, and even elementary particles. At this level, physics is no longer described by deterministic Newton's mechanics, it is described by probabilistic quantum laws. Because of this, computer designers started thinking how to design a reliable computer based on non-deterministic elements -- and this thinking eventually led to the modern ideas and algorithms of quantum computing. So, …
From Quantifying And Propagating Uncertainty To Quantifying And Propagating Both Uncertainty And Reliability: Practice-Motivated Approach To Measurement Planning And Data Processing, Niklas R. Winnewisser, Vladik Kreinovich, Olga Kosheleva
From Quantifying And Propagating Uncertainty To Quantifying And Propagating Both Uncertainty And Reliability: Practice-Motivated Approach To Measurement Planning And Data Processing, Niklas R. Winnewisser, Vladik Kreinovich, Olga Kosheleva
Departmental Technical Reports (CS)
When we process data, it is important to take into account that data comes with uncertainty. There exist techniques for quantifying uncertainty and propagating this uncertainty through the data processing algorithms. However, most of these techniques do not take into account that in real world, measuring instruments are not 100% reliable -- they sometimes malfunction and produce values which are far off from the measured values of the corresponding quantities. How can we take into account both uncertainty and reliability? In this paper, we consider several possible scenarios, and we show, for each scenario, what is the natural way to …
Investigating The Roles Of Plants, Fungi, And Biocrusts In Nutrient Movement Within Dryland Ecosystems, Catherine E. Cort
Investigating The Roles Of Plants, Fungi, And Biocrusts In Nutrient Movement Within Dryland Ecosystems, Catherine E. Cort
Open Access Theses & Dissertations
In dryland ecosystems, plant productivity and microbial decomposition are often separated in space and time due to the asynchronous availability of soil moisture and organic matter inputs. It has been proposed that fungi play a key functional role in connecting these cycles by facilitating movement of water, carbon (C), and nitrogen (N) through a network of shared hyphae between plant roots and biological soil crust (biocrust) communities at the soil surface. This connection, also known as the â??fungal loop,â?? effectively re-couples processes of nutrient release and uptake between primary producers and minimizes ecosystem N losses due to leaching, erosion, and …
Every Feasibly Computable Reals-To-Reals Function Is Feasibly Uniformly Continuous, Olga Kosheleva, Vladik Kreinovich
Every Feasibly Computable Reals-To-Reals Function Is Feasibly Uniformly Continuous, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
It is known that every computable function is continuous; moreover, it is computably continuous in the sense that for every ε > 0, we can compute δ > 0 such that δ-close inputs lead to ε-close outputs. It is also known that not all functions which are, in principle, computable, can actually be computed: indeed, the computation sometimes requires more time than the lifetime of the Universe. A natural question is thus: can the above known result about computable continuity of computable functions be extended to the case when we limit ourselves to feasible computations? In this paper, we prove that this …
From Normal Distribution To What? How To Best Describe Distributions With Known Skewness, Olga Kosheleva, Vladik Kreinovich
From Normal Distribution To What? How To Best Describe Distributions With Known Skewness, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, we only have partial information about the probability distribution -- e.g., all we know is its few moments. In such situations, it is desirable to select one of the possible probability distributions. A natural way to select a distribution from a given class of distributions is the maximum entropy approach. For the case when we know the first two moments, this approach selects the normal distribution. However, when we also know the third central moment -- corresponding to skewness -- a direct application of this approach does not work. Instead, practitioners use several heuristic techniques, techniques …
Every Relu-Based Neural Network Can Be Described By A System Of Takagi-Sugeno Fuzzy Rules: A Theorem, Barnabas Bede, Olga Kosheleva, Vladik Kreinovich
Every Relu-Based Neural Network Can Be Described By A System Of Takagi-Sugeno Fuzzy Rules: A Theorem, Barnabas Bede, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
While modern deep-learning neural networks are very successful, sometimes they make mistakes, and since their results are "black boxes" -- no explanation is provided -- it is difficult to determine which recommendations are erroneous. It is therefore desirable to make the resulting computations explainable, i.e., to describe their results by using commonsense rules. In this paper, we use "fuzzy" techniques -- techniques developed by Lotfi Zadeh to deal with commonsense rules formulated by using imprecise ("fuzzy") words from natural language -- to show that such a rule-based representation is always possible. Our result does not yet provide the desired explainability, …
Smooth Non-Additive Integrals And Measures And Their Potential Applications, Olga Kosheleva, Vladik Kreinovich
Smooth Non-Additive Integrals And Measures And Their Potential Applications, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In this paper, we explain why non-additive integrals and measures are needed, how non-additive integrals and measures are related, how to use them in decision making, and how they can help in fundamental physics. These four topics are covered, correspondingly, in Sections 2-5 of this paper.
When Is A Single "And"-Condition Enough?, Olga Kosheleva, Vladik Kreinovich
When Is A Single "And"-Condition Enough?, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, there are several possible decisions. Any general recommendation means specifying, for each possible decision, conditions under which this decision is recommended. In some cases, a single "and"-condition is sufficient: e.g., a condition under which a patient is recommended to take aspirin is that "the patient has a fever and the patient does not have stomach trouble". In other cases, conditions are more complicated. A natural question is: when is a single "and"-condition enough? In this paper, we provide an answer to this question.
If We Add Axiom Of Choice To Constructive Analysis, We Get Classical Arithmetic: An Exercise In Reverse Constructive Mathematics, Olga Kosheleva, Vladik Kreinovich
If We Add Axiom Of Choice To Constructive Analysis, We Get Classical Arithmetic: An Exercise In Reverse Constructive Mathematics, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
A recent paper in Bulletin of Symbolic Logic reminded that the Axiom of Choice is, in general, false in constructive analysis. This result is an immediate consequence of a theorem -- first proved by Tseytin -- that every computable function is continuous. In this paper, we strengthen the result about the Axiom of Choice by proving that this axiom is as non-constructive as possible: namely, that if we add this axiom to constructive analysis, then we get full classical arithmetic.
Towards A Model Of The Mapping Between English And Spanish Prosody, Jonathan Avila
Towards A Model Of The Mapping Between English And Spanish Prosody, Jonathan Avila
Open Access Theses & Dissertations
Current speech-to-speech translation systems face challenges in effectively translating the nuances of prosody, which plays a pivotal role in conveying speaker intent and stance in dialog. This limitation restricts cross-lingual communication, especially in situations demanding deeper interpersonal understanding. To address this, this research delves into the relationships between prosody and its pragmatic functions, in English and Spanish. First, I discuss a data collection protocol in which bilingual speakers re-enact utterances from an earlier conversation in their other language, then describe an English-Spanish corpus, consisting of 3816 matched utterance pairs. Second, I describe a prosodic dissimilarity metric based on Euclidean distance …
Southern Rio Grande Rift Kinematics And Geochronology, Big Bend Fold Geometry, And The Use Of Real Data In Geoscience Education: Contributions To The Understanding Of Big Bend Geology And To Public Geoscientific Literacy, Jessica Kelsch
Open Access Theses & Dissertations
The Big Bend region of Trans-Pecos Texas preserves a rich record of Rio Grande rifting and Laramide-age contraction that provide intrigue to national and state park visitors and field trips for undergraduate geology students. Despite its well-exposed geologic record, the Big Bend region remains an underutilized natural laboratory for studying these two tectonic events. This dissertation combines structural studies of Rio Grande rift and Laramide structures with public outreach and geoscience education studies focused on the Big Bend region. In Chapter 2, existing extensional-kinematic studies from parts of this region are compiled with new fault kinematic and U-Pb geochronologic data …
Leveraging Agile Software Methodologies Within Software Development To Introduce A Novel Educational Software Methodology, Montserrat Guadalupe Molina
Leveraging Agile Software Methodologies Within Software Development To Introduce A Novel Educational Software Methodology, Montserrat Guadalupe Molina
Open Access Theses & Dissertations
Agile Software Development has been growing increasingly popular in the software engineering industry as a way to produce working software in a quick and people-centered manner. Agile methodologies require practitioners to have strong technical and non-technical skills, such as teamwork, project management, and communication skills. Students graduating from the software engineering discipline have been found to be lacking in these areas, leading to many difficulties faced by recent graduates as they begin their professional careers. Given that Agile Software Development is the most popular software development lifecycle currently used by practitioners in industry, it is important to expose students to …
Sterically Encumbering Ligands For The Synthesis And Stabilization Of Iron Nitride And Iron Oxo Compounds, Asiel Mena
Sterically Encumbering Ligands For The Synthesis And Stabilization Of Iron Nitride And Iron Oxo Compounds, Asiel Mena
Open Access Theses & Dissertations
The study of iron-nitrides has been found to be very attractive due to their potential role in processes like Haber-Bosch and nitrogen fixation by nitrogenase. The role of iron-nitrides in these processes is yet not well understood, and the fact that only handful of terminal iron-nitrides have been isolated or spectroscopically detected motivates us to study this type of systems, since much remains to be learned about the electronic and structural factors that affect the chemistry of the Feâ?¡N bond. Recently in our group, by using a super-bulky guanidinate ligand (LAr*), the obtention of an iron-nitride ([LAr*]FeN(py) (LAr* = (Ar*N)2C(NCtBu2), …
Enhancing Our Understanding Of Ancient Oceans Through The Investigation Of Molybdenum Behavior Under Sulfidic Conditions, Rachel Faye Phillips
Enhancing Our Understanding Of Ancient Oceans Through The Investigation Of Molybdenum Behavior Under Sulfidic Conditions, Rachel Faye Phillips
Open Access Theses & Dissertations
The most abundant trace metal in the ocean today, molybdenum (Mo), exhibits distinct behavior in oxygenated water, where it remains predominantly dissolved, compared to euxinic (i.e., oxygen-free and sulfidic) water, in which it is sequestered into the sediment. This dissimilar behavior allows us to use Mo concentrations and isotopic compositions in sediment to reconstruct marine oxygenation conditions throughout geologic history. However, Mo sequestration mechanisms under euxinic conditions remain unresolved, which limits the accuracy and precision of reconstructions made using Mo signatures in the rock record. For my doctoral research, I experimentally investigated abiotic and biotic Mo sequestration mechanisms under various …
Metrics For Comparison Of Complex Networks, Clarissa Reyes
Metrics For Comparison Of Complex Networks, Clarissa Reyes
Open Access Theses & Dissertations
Heuristic network statistics are used as a preliminary approach to identify change across networks. In networks where there is known node correspondence (KNC), conventional network comparison methods include taking a norm of the difference matrix, or calculating dissimilarity measures like DeltaCon and cut distance. Since different KNC measures provide varying insight to the network comparison problem, we propose employing Rank Score Characteristic Functions (RSCFs) and the rank-score process as a method for reaching a consensus when ranking quantified change across multiple pairs of networks â?? which is particularly useful for ranking change across subpopulations or subgraphs. Additionally, we propose a …
Alteration And Mineralization Of The Deep Extension Of The Giant Chuquicamata Porphyry Copper Deposit, Northern Chile, Claudio Andres Araya Torres
Alteration And Mineralization Of The Deep Extension Of The Giant Chuquicamata Porphyry Copper Deposit, Northern Chile, Claudio Andres Araya Torres
Open Access Theses & Dissertations
Porphyry copper deposits are the major source of copper and molybdenum in the world. The deposits consist of large volumes of rock altered by hydrothermal fluids released by shallow, intermediate composition magma chambers, with metallic mineralization present in veins, breccias, and disseminations; ore grades are typically 0.3-1.0 wt.% Cu. The subject of this study, the Chuquicamata porphyry copper deposit in northern Chile, is one of the most productive such deposits in the world, with over 45 million tons of Cu produced since large scale, open pit mining started early in the XXth century. Current production at Chuquicamata is from an …